The adsorption for H atoms on the Rhn cluster has been systematically investigated by density functional theory. The result indicates that the lowest energy structures of RhnH2 are generated with H atoms being adsorbed on the lowest energy structure of Rhn clusters, and the lowest energy structures of Rhn clusters are not changed by adsorbing H atoms. The total magnetic moment is affected by average bond distance. The chemisorption of H atoms on Rhn clusters belongs to dissociative adsorption. When H2 is absorbed on the Rhn clusters, the stability and chemical action of corresponding clusters are dramatically increased. The second order difference indicates 4 is magic number in RhnH2 and Rhn clusters. Among various possible adsorption sites, bridge site is energetically preferred for n≤5. The hollow site adsorption appears for n≥6.